Many-body Oseen hydrodynamic interactions

We consider the many-sphere hydrodynamic interactions in the incompressible, viscous fluid, under small Reynolds number Re conditions. The interactions are analysed in the framework of the Oseen equation of motion, with the aid of the respective Green tensor, accounting for the convective inertia of the fluid. The hydrodynamic forces, exerted by the fluid on the spheres, are described by means of the multiple scattering series. The properties of the Oseen velocity field of the fluid, generated by the many-sphere hydrodynamic interactions, are contrasted with the features of the respective Stokes velocity field.